Bruce Willis’ daughter, Scout, is a real Die Hard about her right to post topless photos on Instagram.

Photo: Twitter

The perky Hollywood princess took a bare-breasted jaunt around the Lower East Side this week (left and above) to protest the social-media Web site’s banning of nudity.

The 22-year-old — whose mom is “Striptease” star Demi Moore — is boycotting the site, and has posted racy shots of her stroll on Twitter with the hashtag #FreeTheNipple.

One shot features Scout checking out flowers with the caption “Legal in NYC but not on @instagram.” Another shows her on Orchard Street in just a summery skirt with the words: “What @instagram won’t let you see.”

Going topless is, in fact, perfectly legal in New York City.

Scout’s beef started on May 20, when Instagram deleted her photo of a “Babe Bomber” sweat shirt, emblazoned with an image of two topless women.

“Why does @instagram allow photos of heroin being used but deletes a photo of a print of some [attractive women] without tops on???” she tweeted after the deletion. On May 22, she declared her boycott, firing off photos and tweets decrying the company as hypocritical.

One of the many saucy images she tweeted featured a woman in a barely-there swimsuit with the caption: “@instagram pictures of breast cancer survivors have been flagged+deleted but this is super #sick and #hot amiright???”

Since then, she changed her Twitter profile photo to an image of Rihanna sans shirt.

“If you don’t like what you see, simply unfollow me,” she wrote Tuesday. “My comfort with my body should not be dictated by how others perceive me.”

On Wednesday, Instagram defended its no-bare-breast policy to The Post, saying: “We try hard to find a good balance between allowing people to express themselves creatively and keeping Instagram a fun and safe place.”